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Open problems in mathematical physics

2017
*
Physica Scripta
*

We present a list of

doi:10.1088/1402-4896/aa83c1
fatcat:zviukujzvfg5vmb62ynbkeutci
*open*questions*in**mathematical*physics. ... After a historical introduction, a number of*problems**in*a variety of different fields are discussed, with the intention of giving an overall impression of the current status of*mathematical*physics, particularly ... Summary of*problems**in**mathematical*physics The hardest part, perhaps, is making the number of*open*questions*in**mathematical*physics add up to 42. ...##
###
Open Problems in Mathematics with John Nash

2017
*
EMS Newsletter
*

to prepare together the book

doi:10.4171/news/106/13
fatcat:epkjdmywt5f5zpxowo62hpjk24
*Open**Problems**in**Mathematics*. ...*problems**in**mathematics*. ...##
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Mathematical open problems in Projected Entangled Pair States
[article]

2019
*
arXiv
*
pre-print

The aim of this paper is to present, for a broad

arXiv:1903.09439v1
fatcat:e6ejobfwqvc2vgdyhzjckmydym
*mathematical*audience, some*mathematical*questions about PEPS. ... Projected Entangled Pair States (PEPS) are used*in*practice as an efficient parametrization of the set of ground states of quantum many body systems. ... However*in*2D the analogue*problems*are quite*open*. First of all, there is no known solution of the local approximation*problem*. ...##
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Five open problems in compressible mathematical fluid dynamics

2013
*
Methods and Applications of Analysis
*

The

doi:10.4310/maa.2013.v20.n2.a6
fatcat:5kmmrbtqzzaafkqb4chdcuud7y
*problems*below are motivated by some of the works I did*in*the past. They deal with the dynamics of compressible fluids, either viscous or inviscid. ... They are not worth a million dollars, even not a penny, but they are interesting*in*their own. ... The*open**problems*are countless, and our choice of five of them is strongly biased by our own*mathematical*interest and previous research. ...##
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Selection principles in mathematics: A milestone of open problems
[article]

2007
*
arXiv
*
pre-print

We survey some of the major

arXiv:math/0312182v4
fatcat:o3llea6ey5f5xamcivxs3rwtwm
*open**problems*involving selection principles, diagonalizations, and covering properties*in*topology and infinite combinatorics. ... evolving field of*mathematics*. ... This is one of the major*open**problems**in*the field. ...##
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About Open Problems
[chapter]

2014
*
Open Problems in Mathematics and Computational Science
*

about unsolved,

doi:10.1007/978-3-319-10683-0_1
fatcat:bsjz3cnk5vdhphs7zm7xb76m24
*open**problems**in**mathematical*and computation sciences, directly from the scientists who are rigorously investigating them. ... The motivation of the*Open**Problems**in**Mathematical*and Computational Sciences Conference was to enable and encourage the academic community, particularly young researchers and Ph.D. candidates, to hear ... One purpose of the*Open**Problems**in**Mathematical*and Computational Sciences Conference is to encourage, motivate, and excite the*mathematical*and computational sciences community to discuss*open**problems*...##
###
Communication Ability in Resolving Open-Ended Problem in Mathematics

2020
*
International Journal of Multicultural and Multireligious Understanding
*

The purpose of research was to know student's communication abilities

doi:10.18415/ijmmu.v7i7.1771
doaj:0d317862840a469a917ef70f8769a373
fatcat:fj44ubwtszeknjmhwm2gjgzw2a
*in*solving*open*-ended*problems*with the material equation and quadratic function. ... Based on research analysis show that: (1) written communication of the students*in*solving*problems*have different solutions; (2) the student with high communication ability is better at*open*-ended*problem*... One of*problem**in**mathematics*is*mathematics**open**problems*. ...##
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The Discrete Logarithm Problem
[chapter]

2016
*
Open Problems in Mathematics
*

*In*this expository paper we discuss several generalizations of the discrete logarithm

*problem*and we describe various algorithms to compute discrete logarithms. ... For large prime numbers p, computing discrete logarithms of elements of the multiplicative group (Z/pZ) * is at present a very difficult

*problem*. ... Exponential algorithms Following ideas

*in*[11, section 7] , we consider the following general

*problem*. It is a natural extension of the discrete logarithm

*problem*.

*Problem*. ...

##
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Open Tasks in Mathematics: Experiences with one Problem Field

2018
*
Magistra Iadertina
*

With its aid, our purpose is to show how

doi:10.15291/magistra.1487
fatcat:ywlwyu2x7nhntluzx4pei7cdiu
*open*teaching acts*in*practice. ...*In*this paper, the task "Number Triangle" stands for*problem*fields. The*problem*field*in*question is planned by the author to be used*in*the Finnish comprehensive school. ... The*problem*offered me a good structure on the implementation of*open**problems**in*school instruction. ...##
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Using open problems and cooperative methods in mathematics education

2015
*
LUMAT
*

Two aspects are taken into consideration

doi:10.31129/lumat.v3i1.1048
fatcat:i46xkaxinbbt7brgq5lufzo6em
*in*connection with*mathematical**problem*solving:*open**problems*and cooperative teaching. ... Roughly speaking we can differentiate between two main styles*in*teaching*mathematics*: either the focus is on the students or the focus is on*mathematics*as a science. ...*In*our experiment*opening**problems*goes*in*this direction 2. ...##
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The role of open-ended problems in mathematics education

1994
*
Journal of Mathematical Behavior
*

*Open*-ended

*problems*have become a popular educational tool

*in*

*mathematics*education

*in*recent years. ... Since

*mathematical*research is nothing but a daily confrontation with

*open*-ended

*problems*, the introduction of this type of

*problems*to the classroom brings

*mathematical*education one step closer to real ... The isoperimetric inequality is one of the most profound inequalities

*in*

*mathematics*, both

*in*terms of its intrinsic significance and the impact it has exerted on the development of

*mathematics*, past and ...

##
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Hadwiger's Conjecture
[chapter]

2016
*
Open Problems in Mathematics
*

This is a tremendous strengthening of the four-colour theorem, and is probably the most famous

doi:10.1007/978-3-319-32162-2_13
fatcat:v3wuu2dy55cyldjdpens53tuku
*open**problem**in*graph theory. * Supported by ONR grant N00014-10-1-0680 and NSF grant DMS-1265563. ... Introduction The four-colour conjecture (or theorem as it became*in*1976), that every planar graph is 4-colourable, was the central*open**problem**in*graph theory for a hundred years; and its proof is still ... This remains*open*. ...##
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Some open problems in mathematical two-dimensional conformal field theory
[article]

2017
*
arXiv
*
pre-print

We discuss some

arXiv:1606.04493v2
fatcat:g63t64hzifd4jkpyhz7smhgqt4
*open**problems**in*a program of constructing and studying two-dimensional conformal field theories using the representation theory of vertex operator algebras. ...*In*this note, we discuss some*open**problems**in*this program. Some of the*problems*are well known. The others are what the author is interested*in*and believes to be important. ... for the successful solutions of*mathematical*conjectures and*problems*. ...##
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Open Problems in Logical Dynamics
[chapter]

2006
*
Mathematical Problems from Applied Logic I
*

This paper is a survey of conceptual issues and

doi:10.1007/0-387-31072-x_3
fatcat:f5il7g4k6zcdndjrl3ymqaetl4
*open**mathematical**problems*emanating from this development. ... '*Open**problems*'*in*new areas like this may be of several different sorts. ... We mention some*open**problems**in*those areas that seem relevant to our concerns*in*the preceding sections. ...##
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The evolution of mathematical explorations in open-ended problem-solving situations

2005
*
Journal of Mathematical Behavior
*

Focus on Learning

doi:10.1016/j.jmathb.2005.09.007
fatcat:q7nynxggtfay5eivtxafjbue4a
*Problems**in**Mathematics*, 27(3), illustrated and explained several characteristics of the solvers'*mathematical*explorations*in**open*-ended*problem*situations. ... Exploring*mathematical*exploration: How two college students formulated and solved their own*mathematical**problems*? ... Acknowledgements The research discussed*in*this paper was supported,*in*part, by grants from the Spencer Foundation and the University of North Carolina. ...
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